Political values as an optimization problem

How we can use a mathematical framework to understand why people have different policy preferences

John, a libertarian, and Jane, a socialist, get into an argument about the value of the welfare state. John thinks that Jane condones the government trampling over people’s liberty; how much of people’s hard-earned money does she think the government should pilfer? Does she really think it will be used effectively? Conversely, Jane thinks that John is heartless. Is he really that greedy that he’d rather hold onto every possible dollar, even though there are needy families out there who’d get a lot more out of a few extra hundred dollars of his earnings than he would? Both John and Jane want what they think is best for their country and its people, but they’re starting from such different value systems that it’s hard for them to see each other’s core motivations.

I’ve only seen one strong attempt to explain why these motivations differ enough to make it hard for us to understand each other’s points of view. Moral foundations theory, pioneered by Jonathan Haidt and a few other psychologists, ‘proposes that several innate and universally available psychological systems are the foundations of “intuitive ethics.”’ The theory argues that conservatives use five different moral foundations more or less equally, while liberals primarily use two. (Caveat: I haven’t actually read Haidt’s The Righteous Mind, where he expounds on this theory in detail, but I’ve read explanations of the theory and listened to his interview about the topic with Julia Galef on her podcast.) Since conservatives are weighing an additional set of concerns, their preferences won’t always maximize the values of the two foundations that liberals prioritize, thus making liberals think they don’t care about those foundations at all. Conversely, liberals won’t care much about the three foundations they lack that conservatives share, so conservatives may see them as ignoring those foundations that they still find important.

Moral foundations theory is a useful tool, but it’s not always fine-grained enough to answer questions about political preferences. Why do some liberals propose universal basic income as a tool to fight poverty and help workers displaced by automation, while others oppose it? How could it be that a Republican president (Nixon) created the EPA, but now a Republican congressman (Matt Gaetz) wants to abolish it? Liberals have plenty of areas of disagreement with other liberals, and likewise with conservatives. Where do those differences come from?

To answer those questions, we need to take a quick detour into a mathematical framework for solving certain types of problems. The framework is called optimization, and it’s used to either maximize or minimize variable(s) of interest, possibly subject to certain rules called constraints. For example, a business wants to maximize profits, but it has constraints like available capital and adherence to minimum wage laws. If you took a calculus course (in high school or college), you probably saw a few optimization problems. A classic one is a farmer who has a certain amount of fencing and wants to maximize the area enclosed by the fence, so his livestock have the most area in which to roam.

In optimization, the function to be maximized or minimized is called the objective function. So in the farmer example, the objective function is the area enclosed by the fence. More complicated optimization problems can also have multiple objectives. In the business example, the company might actually have other objectives in addition to maximizing present-day profits. They may, for instance, be hoping to get acquired by another business, so they might also want to maximize their attractiveness to that company for acquisition. This form of optimization is called multi-objective optimization, and it’s often solved by considering all solutions along what’s known as a Pareto front. If a solution to the multi-objective optimization problem lies on the Pareto front, there’s no possible change that will improve the outcome for at least one objective without making any objectives worse. So in the business example, the company’s current allocation of resources, pricing, and other business decisions would lie on the Pareto front if they can’t increase profits without decreasing their attractiveness as an acquisition target and vice versa. (Perhaps they could increase present-day profits by taking out a risky loan that would enable them to pay for more advertising today, but the loan’s interest rate is unappealing to their potential acquirer.)

The choice of whether to include a variable as a constraint or an objective is also important. In the business example, the company might decide that they don’t care about increasing their attractiveness to their possible acquirer beyond a certain level. In that case, they’d still be solving a single objective problem (maximizing profits), but with the additional constraint that their attractiveness for acquisition remain above some threshold. The solution to this problem might differ from the multi-objective version, especially if the threshold they chose wasn’t very high.

Now that we have the essentials of optimization in place, we can understand John and Jane’s preferences. John wants to maximize liberty subject to some constraints like the government guaranteeing that people adhere to the non-aggression principle with some probability. A more moderate person with some libertarian leanings might even include keeping poverty below a certain level in their constraints. Jane, on the other hand, wants to minimize poverty and also potentially inequality. Her constraints might include prohibitions on discriminating against people based on immutable characteristics like race.

These frameworks also explain the within-party puzzles I mentioned earlier. The Democrats who support UBI may want to minimize poverty and either don’t include concerns like inflation and incentives to not work in their problem, or leave them at low enough levels in their constraints that they think UBI won’t violate them. The ones who oppose UBI, on the other hand, worry that second-order effects like inflation might violate some of their constraints or worsen the values of some of their objectives. The Republicans who support environmental regulation include environmental protections in their constraints, while the ones who want to abolish the EPA might not consider environmental degradation in their optimization problems at all.

Next time you have a political disagreement with someone, consider your own and your interlocutor’s political preferences as optimization problems. You may find it easier to discuss your disagreements in good faith, and you may also find that your optimization formulation is missing either objectives or constraints that are worth considering.